More congruences from Apery-like formulae

We present some congruences modulo $p^{6-d}$ for sums of the type ${\sum }_{k=0}^{(p-3)\mathrm{/}2}{x}^k\left(\genfrac{}{}{0px}{}{2k}{k}\right)\mathrm{/}(2k+1{)}^d$, for $d=1,2,3$ where $p>5$ is a prime.