Is this right in japanese? (translate)

Does this make sense in Japanese? I am trying to tell the person "next time we definitely should go together"

次は、絶対に一緒に行かなきゃならないね

Is that more of an invitation? Your sentence is OK, but the "should go together" sounds a bit like an obligation rather than inviting.

Maybe you could say:
- 次は、絶対一緒に行こうね。Next time, we've gotta go together/let's definitely go together.
- 次に行くときは、絶対一緒だね。Next time we/I go, it'll definitely be together, right?

What you wrote makes complete sense, but it may be easier to just say
次、一緒に行こう！
sweet and simple