Yes, ikanakute wa ikimasen = I have to go.
Although, there, more adequate would be to use ikEmasen, instead of ikimasen.
Now, let's see, there is a fixed phrase: "~te wa ikemasen/ ~te wa ikenai", which means: "it's no good if...".
So here, ikanakute wa ikemasen = it's no good if I don't go => I have to go. There are a few fixed phrases like this for the meaning: "Have to...", and will take a while to master.
You just need to practice them more and you'll get the hang of it and even understand them in such a way that you won't bother thinking of the literal meaning anymore.