"Nem" and "não" can be used as synonymous in many sentences, but there is a thin difference between them, "nem" would be translated better as "not even". Example: Ela queria que eu lhe telefonasse, mas nem tinha seu número. She wanted me to call her, but I did not even have her number. Furthermore, "nem" can be used as an additive conjuntion in negative sentences, presenting a non-contrasting negative idea, like English "or/nor" while "não" is always an adverb. Não gosto de leite, nem de café. I don't like milk nor coffee. Besides, only "nem" means neither (or either in negative sentences) Não gosto nem de café, nem de leite. I don't like either coffee or milk. Tu não gostas de café?! Nem eu! Don't you like coffee?! Neither do I! When answering a question, you have to use "não". - Tu gostas dela? - Não, não gosto. - Do you like her? - No, I don't. "Não" can also be an interjection: Não! Volta aqui! No! Come back here! I think that's it... I'll write another sentence to show you the little difference: Eu nem vou à festa... I'm not even going to the party... Eu não vou à festa. I'm not going to the party.

nem= nor, neither não= not, no The example you did is a special case, "eu nem sei se..." means "I even don´t know if...", here "nem" means "even don´t", but the normal meaning of "nem" is "neither...nor".