Grammar question on Terence's most famous maxim

Homo sum: humani nihil a me alienum puto.

I’ve been wanted to ask this for some time now but I kept forgetting. In what case is humani? My best guess is that it’s in the genitive. And a me I’m guessing is an ablative of separation. Am I right? So would a literal translation of this be:

I am man: I consider nothing of human alien from me.

That literal translation sure does sound like something a caveman learning English would say, doesn’t it (no offense to any cavemen out there by the way)? But just to be clear, would this be a correct figurative translation:

I am man: I consider nothing that is human alien to me.

Gratias vobis ago.

I think you are right.

This is part of the entry for nihil from Lewis and Short.

“With gen.: nihil mali, Cic. Att. 8, 4, 2: nihil novi, id. Fam. 2, 14, 1: nihil humanarum rerum, id. Red. Quir. 5, 1: nihil est lucri quod me hodie facere mavelim, quam, Plaut. Bacch. 4, 8, 18.—Adjectives also, of the second declension as well as of the third, are not unfrequently joined to nihil in the same case, as nihil honestum, lautum, forte, illustre: nihil exspectatione vestrā dignum dico, Cic. de Or. 1, 31, 137.—”

Since L&S doesn’t actually name the usage, it’s the partitive genitive, quite common with nihil, nihil aquae, no water (lit. nothing of water).