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{a3=b3+c3d3a  =b+c7d \begin{cases}{a^3=b^3+c^3-d^3} \\ {a \ \ =b+c-7d}\end{cases}

Positive integers a,b,c,da,b,c,d satisfy the above system of equations. Find the value of a+b+c+da+b+c+d.

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