Not really complex

Algebra Level 3

Suppose \(x\) is a complex number such that \(4x^2+2x+1=0\). Then,

\[\large x^3+x^6+x^9+x^{12}+\ldots = \frac ab\]

where \(a\) and \( b\) are coprime positive integers. Find the value of \(a+b\).

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