In 3 Nephi 2:14-15 it says:
. . . those Lamanites who had united with the Nephites were numbered among the Nephites; And their curse was taken from them, and their skin became white like unto the Nephites.
According to Hugh Nibley, here's a nice note on race again. If you were a Lamanite who had joined the Nephites, you were now called a Nephite. Did they change their complexion and become white overnight? No, it's a cultural thing. [Hugh W. Nibley, Teachings of the Book of Mormon, Semester 3, p. 276]