Do you know recurrence formula?

Algebra Level 5

a4+b4+c4a3+b3+c3\dfrac{a^4+b^4+c^4}{a^3+b^3+c^3} Let a,b,ca,b,c be the roots of the equation 6x36x23x1=06x^3-6x^2-3x-1=0.

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

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