MathNet 2014 Question 26

Let $ABC$ be a triangle with $AB = 5$, $AC = 4$, $BC = 6$. The angle bisector of $C$ intersects side $AB$ at $X$. Points $M$ and $N$ are drawn on sides $BC$ and $AC$, respectively, such that $\overline{XM} \parallel \overline{AC}$ and $\overline{XN} \parallel \overline{BC}$. Compute the length $MN$.



Supplemental illustration; no extra hypothesis.