Satisfactory reals

Algebra Level pending

The sum of all real numbers \(t\) such that \((3^t-9)^3\)+\((9^t-3)^3\)=\((9^t+3^t-12)^3\) can be represented in the form \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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