Mormons believe that Christ died ONLY for Adam's sin
I don't know where you came up with that idea. That is completely untrue as well.
What kind of proof would be sufficient for you?
the Mormon Church teaches that Adam’s sin was "a necessary step in the plan of life and a great blessing to all of us" (Gospel Principles, p. 33; Book of Mormon — 2 Nephi 2:25; Doctrines of Salvation, vol. 1, pp. 114-115).
Mormon Church teaches that the purpose of the atonement was to bring resurrection and immortality to all people, regardless of whether they receive Christ by faith. Christ’s atonement is only a partial basis for worthiness and eternal life, which also requires obedience to all the commands of the Mormon church, including exclusive Mormon temple rituals (Gospel Principles, pp. 74-75; Mormon Doctrine, p. 669).
Mormon Church teaches that the Bible has been corrupted, is missing many "plain and precious parts" and does not contain the fullness of the Gospel (Book of Mormon — 1 Nephi 13:26-29; Doctrines of Salvation, vol. 3, pp. 190-191).
Jesus and Satan are spirit brothers and we were all born as siblings in heaven to them both, (Mormon Doctrine, p. 163; Gospel Through the Ages, p. 15.)
Jesus' sacrifice was not able to cleanse us from all our sins, (murder and repeated adultery are exceptions), (Journal of Discourses, Vol. 3, p. 247, 1856.)
"Therefore we know that both the Father and the Son are in form and stature perfect men; each of them possesses a tangible body . . . of flesh and bones." (Articles of Faith, by James Talmage, p. 38).
"The birth of the Saviour was as natural as are the births of our children; it was the result of natural action. He partook of flesh and blood - was begotten of his Father, as we were of our fathers." (Journal of Discourses, Vol. 8: p. 115).
"Christ was begotten by an Immortal Father in the same way that mortal men are begotten by mortal fathers" (Mormon Doctrine," by Bruce McConkie, p. 547).
"Christ Not Begotten of Holy Ghost ...Christ was begotten of God. He was not born without the aid of Man, and that Man was God!" (Doctrines of Salvation, Joseph Fielding Smith, 1954, 1:18).
"Elohim is literally the Father of the spirit of Jesus Christ and also of the body in which Jesus Christ performed His mission in the flesh ..." (First Presidency and Council of the Twelve, 1916, God the Father, compiled by Gordon Allred, pg. 150).