Nested Cuberoots

Algebra Level 4

Compute:

\[ \sqrt[3]{54+\sqrt[3]{972+\sqrt[3]{21870+\sqrt[3]{551124+\sqrt[3]{14526054+\cdots}}}}} \]

Details and assumptions: \( n^\text{th}\) term is given by \( 27^n + 3^{2n+1} \).

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