\(\frac{a+b^{22}}{a^2+b^{11}}\)

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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