I couldn't help but laugh.

Literal

I [topic-は] without-laughing [emphasis-は] could-not-endure.

~ずにはいられない is a set grammar pattern meaning 'can't help but do X, can't resist doing X.' Built from the classical negative ~ず (equivalent to ~ない) + に + は + いられない. A double negative: 'could not endure not doing it.' Distinct from ~ざるをえない, which expresses external obligation rather than irresistible impulse.