Stuck with algebra

Question

Given that x and y are positive integers and ( (x^ 1/3) + (y^-1) ) ^ -1 = 5/11 Find the values of x and y. So far, I got the answer through the guess and check method as x = 8 and y = 5, but I don't know the steps, could anyone tell me how to do it step by step?

Answer 1

step 1...flip it over so yu hav (x^1/3 +y^-1)=11/5=2.2 . . . tri & tri agin look like the oenlee thang tu du . . . yu hav 2 dont-nos & just 1 equashun . . . so hope teech made it simpel . . . assume x^1/3 is eezee number such as 1, 2, 3,... . with rite side=2.2, good get tu tri x^1/3=2, so 1/y=0.2, so y=5 . . . note...infinut ansers gotta werk...set x^1/3=1, then get y tu go with that . . . x=1, so 1/y=1.2, so y=1/1.2

Comments

Unfortunately, this method is not legitimate and it is incorrect.
I got my answer today
I'll show you
P.S : You're still using the guess and check method which I don't want to use.