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To simplify the expression, we need to use the rule of exponents that states a^m / a^n = a^(m-n). So, 3^{\frac{11}{6}} / 3^{-\frac{9}{6}} = 3^{\frac{11}{6} - (-\frac{9}{6})} = 3^{\frac{20}{6}} = 3^{\frac{10}{3}}.This simplifies to 3^3 * 3^{\frac{1}{3}} = 27 * \sqrt[3]{3}.However, none of the given options match this result. Therefore, there seems to be an error in the provided options.

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