$$\sqrt[3]{1-\frac{127}{343}}$$ is equal to
$$\sqrt[3]{1-\frac{127}{343}}$$ = $$\sqrt[3]\frac{343-127}{343}$$
= $$\sqrt[3]\frac{216}{343}$$
= $$\frac{6}{7}$$
= 1 - $$\frac{1}{7}$$
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