Do you know recurrence formula?

Algebra Level 5

\[\dfrac{a^4+b^4+c^4}{a^3+b^3+c^3} \]Let \(a,b,c\) be the roots of the equation \(6x^3-6x^2-3x-1=0\).

If the value of the expression above is equal to \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).

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