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If a>b>1a>b>1a>b>1 and logab+611logba=6711,\log_a b+\frac{6}{11}\log_b a=\frac{67}{11},logab+116logba=1167, what is the value of a+b22a2+b11?\frac{a+b^{22}}{a^2+b^{11}}?a2+b11a+b22?
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