In Waring's problem, we have Hua's estimate

$$S(a,b,q) = \sum_{x=1}^q e^{2\pi i (ax^k + bx)/q)} \ll q^{1/2+\epsilon} \gcd(b,q),$$ where $(a,q)=1$.

?Do you know a similar upper bound for the sum $$T(a,b,q) = \sum_{\substack{1 \le x \le q\\ (x,q)=1}} e^{2\pi i (ax^k + bx)/q)}$$ where $(a,q)=1$, which appears in Waring-Goldbach problem.