In \(\triangle{ABC}\), \(BC=a \text{ cm}, AC=b \text{ cm},\) and \(AB=c \text{ cm}.\) Given that \(\frac{a^2+b^2}{c^2}=2011\), find the value of

\[\frac{\cot C}{\cot A+\cot B}.\]

This problem is not original.

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