Problem - High Score

You are playing a game with $n$ rooms and $m$ tunnels. Each tunnel goes from room $a$ to room $b$ and changes your score by $x$ (which can be negative). You start in room $1$ and want to reach room $n$. What is the maximum score you can get?

This looks like longest path on a DAG, but the graph might have cycles. If there is a positive cycle reachable from room $1$ that can reach room $n$, you can loop forever and get infinite score.