As my good friend Mr. Mo pointed out to me, there is a secret subtext to this song. Remember Mick Jagger was a student of Economics, no dummy. So using a double-negative was a conscious choice.
Really what Mick is telling us when he says he "can't get no satisfaction," is that he is extremely, immensely, supremely satisfied. There is no way he can be unsatisfied! This song was a huge hit on the charts.
It's dressed up with a fuzz tone guitar, and it's snappy, but really it's not far from the blues. It's kind of a dressed up, popped up blues. And it made the boys big time r&r stars!