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Find the value of the expression

### Solution

\[\begin{aligned}
&a=8+3 \sqrt{21} \\\\
&b=8-3 \sqrt{21}
\end{aligned}\]

Notice \(x=1\) is a solution, Thus \((x-1)\) is a factor: \[(x-1)\left(x^{2}+x+16\right)=0\]

Therefore \[\large \sqrt[3]{8+3 \sqrt{21}}+\sqrt[3]{8-3 \sqrt{21}}=1\]

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