Sums of a square and a cube

Question

I’ve recently found this problem, and I have no idea how to solve it. I would be grateful for any ideas. Let $f(n)$ denote the number of non-negative integers that can be represented as the sum of a square and a non-negative cube, both less than $n$; that is, $f(n)=|\{a^2+b^3 \; | \; a^2<n, 0\leq b^3 <n\}|$. Prove that $f(n) \sim n^{5/6}$, that is, $\lim \limits_{n \to \infty} \frac{f(n)}{n^{5/6}}=1$. My first idea was to try and write something like if $a^3+b^2=c^3+d^2$, then $(a-c)(a^2+ac+c^2)=a^3-c^3=d^2-b^2=(d-b)(d+b)$, but I couldn’t get any further. Any comments are much appreciated!