The area (in sq. units) of the part of circle $x ^ { 2 } + y ^ { 2 } = 169$ which is below the line $5 x - y = 13$ 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