The answer is 1056. Once a factor $2^{20}$ has been collected under the fourth root, one is led to compute $\sqrt[4]{1+2^{7}+2^{11}+2^{12}+2^{17}+2^{20}}$. At this point it is possible to recognize in the expression under the root the square of the trinomial $1+2^{6}+2^{10}=(2^{5}+1)^{2}$ or to directly verify that it is the fourth power of $2^{5}+1$. The expression as a whole is therefore equal to $2^{5}(2^{5}+1)$, that is 1056.