Advanced Number Theory · Superchallenge problem

In triangle $ABC$, point $D$ lies on side $BC$ with $BD = 8$ and $DC = 12$, and $M$ is the midpoint of side $AC$. Line $DM$ extended meets line $AB$ at the point $X$. Then $\dfrac{AX}{XB} = \dfrac{m}{n}$ for relatively prime positive integers $m$ and $n$. Find $m + n$.