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Algebra Level 3

\[\begin{eqnarray} \frac{a^3 + 1}{a^5 - a^4 - a^3 +a^2 } \end{eqnarray} \]

Let \(a\) be one of the roots of the equation \( x^2-x-4=0\). The value of the expression above is a form of \( \dfrac{m}{n} \). Submit your answer as \( m+n\).


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