Would try to develop a relationship with someone who doesn't have much in common with you?

I like this girl, but the only downside is that a) she has mainly different tastes in music and b) isn't into any sports anymore. She has read tons of books (I've only started reaing recently and have only read the, like, big ones, eg. Harry Potter, LOTR etc). But she has a superb personality and is really attractive (but not at all sluttish like most girls where I live!).