Ratio of Sides

Triangle $ABC$ has side lengths $a, b$ and $c$ which satisfy $\frac{a+b}{11}=\frac{b+c}{12}=\frac{c+a}{13}$ . If $\sin A:\sin B:\sin C$ can be expressed as an irreducible ratio $p:q:r$ , where $p$ , $q$ and $r$ are positive integers, what is the value of $p+q+r?$