An Eccentricity from a Focal Sum

The hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ ($a>0$, $b>0$) has left and right foci $F_1$, $F_2$. The parabola $y^2=2px$ ($p>0$) has focus $F_2$, and meets the hyperbola at a point $P$ in the first quadrant. If $|PF_1|+|PF_2|=3|F_1F_2|$, find the eccentricity $e$ of the hyperbola.