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For any two-digit positive integer $\overline {ab}$, it is sabroso if $11a+11b$ is a perfect square, so $a+b=11k^2$ for some positive integer $k$.
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A two-digit positive integer is called an Atiab Number if, when it is added to the number obtained after exchanging the places of it's digits, the sum obtained is a square number. For example, $83$ is an Atiab Number since $83+38=121=11^2$. Find the sum of all possible Atiab Numbers of two digits.
Number Theory
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