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In this paper, we establish improved effective irrationality measures forcertain numbers of the form $\sqrt[3]{n}$, using approximations obtained fromhypergeometric functions. These results are very close to the best possibleusing this method. We are able to obtain these results by determining veryprecise arithmetic information about the denominators of the coefficients ofthese hypergeometric functions. Improved bounds for $\theta(k,l;x)$ and$\psi(k,l;x)$ for $k=1,3,4,6$ are also presented.

Rational approximations to $\sqrt[3]{2}$ and other algebraic numbers revisited