Maths problem help needed

Where do I start on a problem like:

Find all possible pairs (a,b) of integers such that a[cubed] = 5b[cubed]

a³ = 5b³
a³ / b³ = 5
(a/b)³ = 5
a/b = ∛5
So the ratio of a and b should be ∛5 (cube root of 5)

Possible pairs are :
a = 1, b = ∛5
a = 2, b = 2 ∛5
a = 3, b = 3∛5

and so on....

a^3/b^3=5
a^3=b^3*5
a/b=5^(1/3)=1.709975946676696989353108…
you are unlikely to get a satisfactory answer.