2011 AIME II Problem 4

In triangle A B C, A B=\frac{20}{11} A C. The angle bisector of \angle A intersects \overline{B C} at point D,
and point M is the midpoint of \overline{A D}. Let P be the point of intersection of
\overline{A C} and line B M. The ratio of C P to P A can be expressed in the form \frac{m}{n}, where m and
n are relatively prime positive integers. Find m+n.