A median and an altitude

$\triangle ABC$ has side lengths $|AB|=3$ , $|BC|=7$ , and $|AC|=8$ . Let $E$ be the midpoint of $AC$ . The altitude from $A$ to $BC$ and the median from $B$ to $AC$ cut each other at $X$ . Find $m+n$ if $\dfrac{|BX|}{|XE|}$ can be expressed as $\dfrac {m}{n}$ , where $m$ and $n$ are coprime positive integers.