$$(y+6)^3 - (y+24)=x^2$$
I need an integer solution for (x,y) such that it satisfies the above equation. I tried analytical ways but couldn't find any solution. Online plotting tools (like Desmos) could also not get a solution up to y=36. So, it would be wonderful if somebody could come up with a solution where both x and y are positive integers (either methodically or by chance).
Actually, any solution (x,y) would actually satisfy this nested-radical given by:
$$y=\sqrt[3]{x+\sqrt[3]{x^2+\sqrt[3]{x^3+\sqrt[3]{x^4+\sqrt[3]{x^5...}}}}}$$