A physical trainer calculates that a client's heart rate $H$ (in beats per minute) after $m$ minutes of intense exercise satisfies $|H - 150| < 20$. If the client starts at $m=0$ with $H=135$, and their heart rate increases linearly such that $H(m) = 135 + 5m$, for what range of $m$ is the condition $|H - 150| < 20$ satisfied?