Your sentence is correct but awkward. I think it should be "need to":
- Nobody needs to know everything, but everybody needs to want to know everything.
The 2nd clause is still awkward, though:
- Nobody needs to know everything, but they should /want/ to know everything.
(In speech, you'd stress the word "want", in writing you'd italicize it for emphasis.)
I think (but could be wrong) there is a similar, slight difference between Spanish "tener/hay que" and "necesitar":
- tengo que hacerlo => I must do it
- necesito que hacerlo => I need to do it