Algebra Level 5

Compute:

$\sqrt[3]{4+1^2\sqrt[3]{10+3^2\sqrt[3]{16+5^2\sqrt[3]{22+7^2\sqrt[3]{28+\cdots}}}}}$

Details and assumptions:

The first sequence $4, 10, 16, 22, \ldots$ is an arithmetic progression, while the second one $1^2, 3^2, 5^2, 7^2, \ldots$ is the sequence of odd squares.

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