I have found this pretty identity involving cube roots, first stated by Ramanujan:
$$ \sqrt{m(4m-8n)^{\frac13} + n(4m+n)^{\frac13}} = (4m+n)^{\frac23} + (4(m-2n)(4m+n))^{\frac13}- (2(m-2n))^{\frac23}. $$
So I ask if there is any method to create similar identities?