While 5'9" is "about average for a British male", as others have said, the OP likely doesn't want to be a bit above average in a sense that includes all men one and two generations older than him and South and East Asians and so forth. He will want to be average for the 20 year old white guy I guess him to be. And 5'11" is about that.
Well 5 ft 11 is not so tall that you have to work alot harder to see a difference in muscle mass (with the mass being spread over a taller frame) but not so small that other people are towering over you all the time. If you think about it, it's a good height to be for a guy who wants to build muscle. But maybe you don't.
Personally I'm 5 ft 8 and I tend to be able to see increases in muscle mass pretty quickly. The only time it annoys me is on nights out (which are rare anyway) wherein all the girls are wearing skyscraper heels. brb injecting growth hormone.