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We use the Malliavin calculus and the so-called Stein's method on Wiener chaos introduced by Nourdin and Peccati \\cite{NP09} to derive, in the case when $0<HK\\leq3/4$, Berry-Ess\\'een-type bounds for the Kolmogorov distance between the law of the correct renormalization $V_n$ of $Z_n$ and the standard normal law. 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