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In this paper, it is proved that, for $12\\leqslant b\\leqslant 35$ and for every sufficiently large odd integer $N$, the equation \\begin{equation*}\n  N=x^2+p_1^3+p_2^3+p_3^3+p_4^3+p_5^4+p_6^b \\end{equation*} is solvable with $x$ being an almost-prime $\\mathcal{P}_{r(b)}$ and the other variables primes, where $r(b)$ is defined in the Theorem. 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