A problem by minimario minimario

Right triangle $ABC$ with right angle at $B$ has $\angle BAC=50^\circ$ and $\angle ACB=40^\circ$ . Points $D, E$ lie on side $BC$ such that $DE=9000 \text{ cm}, \angle DAE=10^\circ$ and $\angle BAD=\angle EAC$ . The ratio $\frac{DB}{CE}$ can be expressed in the form $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .