One of Euler’s conjectures was disproved in the 1960 s by three American mathematicians when they showed that there is a positive integer n such that

133^{5}+110^{5}+84^{5}+27^{5}=n^{5} .

Find the value of n.

One of Euler’s conjectures was disproved in the 1960 s by three American mathematicians when they showed that there is a positive integer n such that

133^{5}+110^{5}+84^{5}+27^{5}=n^{5} .

Find the value of n.