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\left(-2+3\left(-2\right)\right)\times 1+\sqrt[3]{1+3^{2}}
Divide -10 by 5 to get -2.
\left(-2-6\right)\times 1+\sqrt[3]{1+3^{2}}
Multiply 3 and -2 to get -6.
-8+\sqrt[3]{1+3^{2}}
Subtract 6 from -2 to get -8.
-8+\sqrt[3]{1+9}
Calculate 3 to the power of 2 and get 9.
-8+\sqrt[3]{10}
Add 1 and 9 to get 10.