There are many beautiful infinite radical equations, some relatively straightforward, some much more subtle: $$ x = \sqrt{ x \sqrt{ x \sqrt{ x \sqrt{ \cdots } } } } $$ $$ \sqrt{2} = \sqrt{ 2/2 + \sqrt{ 2/2^2 + \sqrt{ 2/2^4 + + \sqrt{ 2/2^8 + \sqrt{ \cdots}}}}} $$ $$ 3 = \sqrt{1 + 2\sqrt{1 + 3\sqrt{ 1 + 4\sqrt{ \cdots }}}} $$
But I have seen far fewer analogous equations for $n$-roots. Here is one: $$ 2 = \sqrt[3]{6 + \sqrt[3]{6 + \sqrt[3]{6 + \sqrt[3]{\cdots}}}} $$
My question is:
Q. Are there truly "more" beautiful infinite radical equations, or is it just our natural gravitation toward the simpler square-root equations that leads to collections emphasizing radicals?
I am aware this question is vague, but perhaps some nevertheless have insights.