For liability reasons, let me be clear to anyone (especially from APEGA) reading along: I don't dole out professional advice on the internet. Do not construe anything I write on this forum to be professional advice. If you need professional advice, seek the advice of a professional.
(Which could be me... but not on this forum...)
That said, do you recall how far down the line the snake was when the end broke off? If you were anywhere near the connection to the main out in the street/alley, I'd say don't worry about it. If it was in the house... you could just pop the nearest cleanout and rent another snake to retrieve the broken end.