Lines & Planes in Space · Superchallenge problem

A light ray leaves $(3, 2, 5)$ in the direction $\langle -1, -1, -2\rangle$, hits the mirror plane $x + y + z = 1$ and reflects (angle of incidence equals angle of reflection). The reflected ray later reaches the plane $z = 3$. Find the $x$-coordinate of the point where it does.