Find a formula for the inverse of the following function, if possible.
$$s(x)=\sqrt[3]{5x+1}$$
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$$s^{-1}(x)=$$
does not have an inverse function

Step 1 ：The function given is a cubic root function, which is a one-to-one function. This means that it does have an inverse. To find the inverse of a function, we need to switch the x and y (or in this case, s(x)) values and solve for y.

Step 2 ：In this case, we have $s(x)=(5x+1{)}^{1/3}$. If we switch x and s(x), we get $x=(5s(x)+1{)}^{1/3}$. Now we just need to solve this equation for s(x) to find the inverse function.

Step 3 ：We start with $x=(5s(x)+1{)}^{1/3}$. To isolate s(x), we can cube both sides to get rid of the cubic root, which gives $x^3=5s(x)+1$. Then, we can subtract 1 from both sides and divide by 5 to solve for s(x).

Step 4 ：Final Answer: The inverse function of s(x) is $\boxed{{\displaystyle s^{-1}(x)=\frac{x^3-1}{5}}}$