100 Followers Problem

Geometry Level 4

\[\large \sum_{k=1}^{35} \sin \left(5k^\circ \right) = \tan \left(\frac {m}{n}\right)^\circ\].

The equation above holds true for coprime positive integers \(m\) and \(n\), where \(\dfrac {m}{n} < 90\). Find \(m+n\).