Ratio of Sides

Level pending

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 \(p+q+r?\)

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