\[\begin{cases} x + 2y = p + 6 \\ 2x - y = 25 - 2p \end{cases} \]

Solve the system of equations above, for positive integers \( (x,y,p) \). If the answer is in the form of \( (x_1 , y_1 , p_1) , (x_2 , y_2 , p_2) , ... , (x_n , y_n , p_n) \), find \( \displaystyle \sum_{m=1}^n ( x_m + y_m + p_m ) \).

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