The area (in sq. units) of the part of the 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 \( \alpha , \beta \) are coprime numbers. Then \( \alpha + \beta \) is equal to __________.
