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Michael Rapaport is finally coming clean about his beef with LeBron James ﻿... saying it all goes back to how The King treated his 2 sons back in the day.

"When they ran into LeBron, he dissed my kids," Rapaport said on The Breakfast Club. "He gave 'em the f**kin' Heisman and turned his back to them."

Mike thinks 'Bron held a grudge against him 'cause their friends of friends had a bad falling out ... and took it out on his boys.

Rapaport couldn't believe it -- and says that makes LBJ the worst celeb he's ever met.

"It has nothing to do with a 10 and an 8-year-old ... don't play me and my kids."