2014 HMMT November General Round Problem 6

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.

Answers are checked by value, so any equivalent form is accepted: 1/2, \frac{1}{2} and 0.5 all count as the same answer.

Full credit goes to HMMT for authoring these problems. This problem is from the November 2014 contest; the official solution is available on the HMMT archive. HMMT is not affiliated with or endorsing TopsOJ in any way.