Explicit diophantine approximation of $2^{1/3}$ and similar algebraics

Given an algebraic number $x$ and $\lambda>2$, there are only finitely many integers $p,q$ with $|x-p/q| < 1/q^\lambda$. We make this explicit for a few algebraic $x$ using the apparatus of G. V. Chudnovsky. Specifically, we make explicit an effective result of Chudnovsky.

Kevin O'Bryant