Length ratios

In $\triangle ABC$ , $AB=2$ , $AC=4$ , and $BC=5$ . Let $B'$ be the reflection of point $B$ about $C$ , and let $G$ be the centroid of the triangle. There exist points $P$ and $Q$ on $AG$ and $B'C$ respectively such that $\dfrac{AP}{PG}=\dfrac{B'Q}{QC}=3.$ If $B'P$ and $AQ$ intersect at $X$ , and $M$ is the midpoint of $BC$ , $MX$ can be written in the form $\dfrac{\sqrt{m}}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .