$Evaluate $\frac{1}{2 \pi i}\int_{|x|=1} \frac{z^{11}}{12z^{12}-4z^9+2z^6-4z^3+1}dz$$

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Evaluate $$\frac{1}{2 \pi i}\int_{|x|=1} \frac{z^{11}}{12z^{12}-4z^9+2z^6-4z^3+1}dz,$$

by using residue theory.

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