Find all solutions to the inequality \[\sqrt[3]{x}+ \frac{2}{\sqrt[3]{x}+ 3} \le 0,\]giving your answer in interval notation.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all solutions to the inequality \[\sqrt[3]{x}+ \frac{2}{\sqrt[3]{x}+ 3} \le 0,\]giving your answer in interval notation.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty, -27) \cup [-8, -1]
Find all solutions to the inequality \[\sqrt[3]{x}+ \frac{2}{\sqrt[3]{x}+ 3} \le 0,\]giving your answer in interval notation.
train