Too many summations

Algebra Level 4

\[ \large \sum_{n=1}^j M_n = j, \sum_{n=1}^j A_n = j^2, \sum_{n=1}^j T_n = j^3, \sum_{n=1}^j H_n = j^4 \]

Given that \(M_n, A_n, T_n, H_n\) are polynomials expressed in terms of \(n\) such that the equations above holds true. If \(M_j + A_j +T_j + H_j = xj^3 - yj^2+yj + z\) for constants \(x,y\) and \(z\), find the value of \(x+y+z\).

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