Reflected line

Geometry Level 5

A ray of light is sent along the line $$2x-3y=5$$. After reflecting across the line $$x+y=1$$ it enters the opposite side by turning $$15^{o}$$ away from the line $$x+y=1$$, The slope of line along which the reflected ray travels is

$m= \frac{ a \sqrt{b} - c } { d }$

where $$a,b,c,d$$ are co prime natural numbers, and $$b$$ is square free.

Find $$a + b + c + d$$.

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