An Eccentricity From a Midline

The line $x - 3y + m = 0$ ($m \ne 0$) meets the asymptotes of the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ ($a, b > 0$) at points $A$ and $B$. If $P(m, 0)$ satisfies $|PA| = |PB|$, find the eccentricity.