I haven't heard the Stones "LIke A Rolling Stone" but I'm not surprised they they did it. Date?

Mick and Keith were big fans, especially in the 60s, Keith probably still is. (Remember the Live Aid fiasco). I recall a report in "Melody Maker" around 1966 of Chris Jagger, Mick's brother, getting off a flight from the States waving an album, shouting, "I've got the new Dylan, I've got the new Dylan"! (Think it was Blonde on Blonde).