1. **State the problem:** Find the inverse function $f^{-1}(x)$ of the function $$f(x) = \frac{-6x + 11}{8x - 5}.$$\n\n2. **Recall the method to find an inverse:** To find $f^{-1}(x)$, we start by replacing $f(x)$ with $y$, then solve for $x$ in terms of $y$, and finally swap $x$ and $y$.\n\n3. **Start with the equation:** $$y = \frac{-6x + 11}{8x - 5}.$$\n\n4. **Multiply both sides by the denominator to clear the fraction:** $$y(8x - 5) = -6x + 11.$$\n\n5. **Distribute $y$ on the left side:** $$8xy - 5y = -6x + 11.$$\n\n6. **Group all terms involving $x$ on one side:** $$8xy + 6x = 5y + 11.$$\n\n7. **Factor out $x$ on the left side:** $$x(8y + 6) = 5y + 11.$$\n\n8. **Solve for $x$:** $$x = \frac{5y + 11}{8y + 6}.$$\n\n9. **Swap $x$ and $y$ to get the inverse function:** $$y = \frac{5x + 11}{8x + 6}.$$\n\n10. **Conclusion:** The inverse function is $$f^{-1}(x) = \frac{5x + 11}{8x + 6}.$$\n\n**Your work is correct!** You correctly found the inverse function by isolating $x$ and swapping variables.