An algebra problem by Abhay Kumar

Algebra Level 5

\[ \dfrac{(a^3+b^3+c^3)^2 (a^4+b^4+c^4)}{(a^5+b^5+c^5)^2} \]

Given \(a, b\) and \( c\) satisfy \( a + b + c = 0\) and \( a^5 + b^5 + c^5 \neq 0 \), the value of the above expression can be expressed as \(\dfrac mn\), where \(m\) and \(n\) are coprime positive integers, calculate the value of \(m+n\).

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