Question 1198694
Given, 
Cube root of x + Cube root of y = 128
{{{x^(1/3)+y^(1/3)=128}}} .................(1)

Also,
{{{1/(x^3) + 1/(y^3) = 2}}} .......(2)

From equation (1), we can write,

y^(1/3) = 128 - x^(1/3)

Now replace y^(1/3)  in second equation,

{{{1/x^3 + 1/((128 - x^(1/3)))^3= 2}}}

On simplification we get cubic equation in x^(1/3)

3 * x^(1/3)^4 - 8192 * (x^(1/3)) + 2097152 = 0

On solving this equation, we get x^(1/3)= 32

Now replace this value in equation (1),

y^(1/3) = 128 - 32 = 96

 numbers are x = 32^3 = 32768 and y = 96^3 = 884736.