# Roots Everywhere

Algebra Level 5

$\sqrt[4] {x ^ 5 + 48 \sqrt[3] {3} - 96 \sqrt[3] {9}} = \sqrt[5] {x ^ 4 - 48 \sqrt[3] {3} + 96 \sqrt[3] {9}}$

If real $$x$$ satisfies the equation above, then find the value of the infinite root:

$\sqrt[3] {x ^ 3 + \sqrt[3] {x ^ 3 + \sqrt[3] {x ^ 3 + \cdots } } }$

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