The area (in sq. units) of the part of circle $x^2+y^2=169$ which is below the line 5x-y=13 is $\frac{\pi \alpha}{2 \beta}-\frac{65}{2}+$$\frac{\alpha}{\beta} \sin ^{-1}\left(\frac{12}{13}\right)$ where 𝛼,𝛽 are coprime numbers. Then 𝛼+𝛽 is equal to
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