I think it all depends upon what you mean by salvation. If "salvation" means nothing more to you than avoiding eternal damnation, then you are not understanding the word the way Latter-day Saints do. We see the word "salvation" as having different meanings, depending upon the context. I apologize, but I'm going to quote some scripture here, but if I'm going to explain what I just said, I'm going to have to.
1 Corinthians 15:22 says, "For as in Adam all die, even so in Christ shall all be made alive." This seems to me to be a pretty clear statement that death will be permanent for no one. Everyone who had ever lived will be resurrected from the dead. All will be made alive, regardless of their good works, bad deeds, faith or anything else. And this assurance of salvation from an everlasting death is made possible solely through Jesus Christ's Atonement. None of us could possibly raise ourselves from the dead. We have Jesus Christ to thank for that salvation.
Then there is salvation from "Hell." A great many Christians believe that most will ultimately go to Hell because, after all, Matthew 7:14 states, "Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it." Mormons don't believe that this means most will end up in Hell, but that there will be few who find what we refer to as "the fullness of salvation" which is life eternal in the presence of God. We understand that Heaven is not a one-size-fits-all kind of place and that there will be varying degrees of glory in the resurrection. 1 Corinthians 15:40-42 reads, "There are also celestial bodies, and bodies terrestrial: but the glory of the celestial is one, and the glory of the terrestrial is another. There is one glory of the sun, and another glory of the moon, and another glory of the stars: for one star differeth from another star in glory. So also is the resurrection of the dead." Between the glory of the sun and the glory of the stars, there is quite a difference. To end up anywhere in Heaven is to be "saved," according to our understanding, and we believe that most of the people who have ever lived will end up in one of the three different degrees of glory. Romans 14:11 indicates that "
every knee shall bow to me, and
every tongue shall confess to God."
Of course, we have all known of some very wicked people who have died without faith in Christ. But as my favorite LDS Apostle, Dieter F. Uchtdorf, has said, "The more we learn about the gospel of Jesus Christ, the more we realize that endings here in mortality are not endings at all. They are merely interruptions—temporary pauses that one day will seem small compared to the eternal joy awaiting the faithful." We do not believe that death marks the final curtain, and there are many people who will come to know Christ during the period of time between their death and their resurrection. Ultimately everyone will acknowledge that Jesus Christ is their Savior, and with the exception of a very few, all will be "saved" from eternal torment.
Jesus Christ did say, however, on a number of occasions, that our works are important. They are not only important but they are critical to our receiving the greatest of all the blessings our Father in Heaven has set aside from us. Here are just a handful of scriptures that make it absolutely clear that our works will be rewarded:
Matthew 7:21 Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but
he that doeth the will of my Father which is in heaven.
Matthew 16:27 For the Son of man shall come in the glory of his Father with his angels; and then
he shall reward every man according to his works.
John 15:10 Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but
he that doeth the will of my Father which is in heaven.
Romans 2:12-13 For as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law; for
not the hearers of the law are just before God, but the doers of the law shall be justified.
2Timothy: 2-19 Nevertheless, the foundation of God standeth sure, having the seal, The Lord knoweth them that are his. And,
let every one that nameth the name of Christ depart from iniquity.
Hebrews 5:9 And being made perfect,
he became the author of eternal salvation unto all them that obey him.
James 2:20-24 But wilt thou know, O vain man, that
faith without works is dead? Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar? Seest thou how faith wrought with his works, and
by works was faith made perfect? Ye see then how that
by works a man is justified, and not by faith only.
So, in short, we believe that we are saved from physical death regardless of our works, but that we may receive the fullness of salvation only through our joint efforts with our Savior. We believe that God doesn't just want to bring us back to Him, but that He wants to bring us back to Him better than we started out.