Find the domain of the function $z(x) = \sqrt[3]{x - 1} + \sqrt[3]{8 - x}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the domain of the function $z(x) = \sqrt[3]{x - 1} + \sqrt[3]{8 - x}.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty,\infty)
Find the domain of the function $z(x) = \sqrt[3]{x - 1} + \sqrt[3]{8 - x}.$
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