Question 4
In triangle $ABC,$ $AB = \frac{20}{11} AC.$ The angle bisector of angle $A$ intersects $\overline{BC}$ at point $D,$ and point $M$ is the midpoint of $\overline{AD}.$ Let $P$ be the point of intersection of $\overline{AC}$ and line $BM.$ The ratio of $CP$ to $PA$ can be expressed in the form $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$