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\sqrt[3]{61+\sqrt[3]{25+2}}
Calculate \sqrt[3]{8} and get 2.
\sqrt[3]{61+\sqrt[3]{27}}
Add 25 and 2 to get 27.
\sqrt[3]{61+3}
Calculate \sqrt[3]{27} and get 3.
\sqrt[3]{64}
Add 61 and 3 to get 64.
4
Calculate \sqrt[3]{64} and get 4.