In a triangle \( A B C \), if the sides \( \mathrm{a}, \mathrm{b}, \mathrm{c} \) are the roots o...

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In a triangle \( A B C \), if the sides \( \mathrm{a}, \mathrm{b}, \mathrm{c} \) are the roots of \( \mathrm{x}^{3}- \) \( 11 x^{2}+38 x-40=0 \). If the value of \( \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c} \) - can be expressed as a rational number as \( \frac{m}{n} \) in the lowest form then find the value of \( (m+n) \)
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