A problem by minimario minimario

Level pending

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 \( m+n \).

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