The Green-Tao theorem for Piatetski-Shapiro primes

Let $m\geq 3$. Suppose that $$1-2^{-2^{m^24^m}}<\gamma<1.$$ Then the set $$\{p\text{ prime}:\, p=[n^{\frac1\gamma}]\text{ for some }n\in{\mathbb N}\}$$ contains infinitely many non-trivial $m$-term arithmetic progressions.