TxO Math Bowl 2024 - Guts Contest - Set 9 Problem 2

Let ABC be a triangle with AB = 16, CA = 11, BC = 7. The incircle touches AB and BC at F and D, respectively. Let X be a point on segment AF and let DX intersect CF at G. Let BG and AC intersect at H. XH is parallel to FC. Let HC be \frac{a}{b} where a and b are relatively prime positive integers. Find a + b.