# $$\frac{a+b^{22}}{a^2+b^{11}}$$

Algebra Level 2

If $$a>b>1$$ and $\log_a b+\frac{6}{11}\log_b a=\frac{67}{11},$ what is the value of $\frac{a+b^{22}}{a^2+b^{11}}?$

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