# Reminds of Newton?

Algebra Level 4

$\begin{cases} a+b+c=1 \\ a^2+b^2+c^2=2^2 \\ a^3 + b^3+c^3 = 3^2 \end{cases}$

Given that $$a,b$$ and $$c$$ are complex numbers satisfying the system of equations above. If the value of $$\dfrac1{a^3} + \dfrac1{b^3} + \dfrac1{c^3}$$ is equal to $$\dfrac pq$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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