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Let $a$ and $b$ be the roots of the equation $x^2 - 10cx - 11d = 0$. Also, $c$ and $d$ are the roots of the equation $x^2 - 10ax - 11b = 0$.

Assuming $a, b, c$ and $d$ are distinct and non-zero, find the value of $a + b + c+ d$.

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