A median and an altitude

Geometry Level pending

\(\triangle ABC\) 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.

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