I read a manga were it translated しょうがねぇ as "fine," but it doesn't make sense contextually and "it can't be helped" would make much more sense .
I think that your question is already answered here, but I'll include the highlights here.
しょうがない and しょうがねぇ are identical in definition. What you are noticing here is a subtle difference in conjugation.
しょうがない is defined by jisho.org as
it cannot be helped;it is inevitable;there is no point (doing something about it;(etc.). When you look up the definition of しょうがねぇ on jisho.org, your top result is the listing for しょうがない.
This happens all the time with い-type adjectives (and ない). The purpose of the grammar is to show a little more emotion, but sometimes it is also used for the sake of being informal. It should be noted that you should not use this grammar in situations where you are trying to use polite or formal speech, because it is neither polite nor formal.
Using this grammar is easy. Simply turn the い sound into the え sound. For example:
すごい ー＞ すげぇ (you will also see すげー)
じゃない ー＞ じゃねぇ (or じゃねー)
やばい ー＞ やべぇ
You will encounter this grammar regularly in informal speech, anime, and manga. I would not use this in formal/polite speech.
They are the same. The only difference is しょうがねぇ is more casual - almost lighthearted, poking fun at the situation.
For example: “There’s nothing we can do about it.” vs “Ain’t sh*t that can be done.”
(Im working in Japanese and in my department there’s an eccentric guy that says しょうがねぇ a lot (and laughs after he says it) and a strict woman that would never say it, and only use しょうがない when agitated.
The guy might say something like, “We missed the deadline, but the other team wasn’t ready anyway. しょうがねぇ〜 and then crack up laughing.