1. **State the problem:** Simplify the expression $-23 \pm \frac{\sqrt{-60}}{6}$. 2. **Recall the formula and rules:** The square root of a negative number involves imaginary numbers. Specifically, $\sqrt{-a} = i\sqrt{a}$ where $i$ is the imaginary unit with $i^2 = -1$. 3. **Simplify the square root:** $$\sqrt{-60} = \sqrt{-1 \times 60} = \sqrt{-1} \times \sqrt{60} = i \sqrt{60}$$ 4. **Simplify $\sqrt{60}$:** $$\sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15}$$ 5. **Substitute back:** $$-23 \pm \frac{i \times 2\sqrt{15}}{6}$$ 6. **Simplify the fraction:** $$-23 \pm \frac{2i\sqrt{15}}{6} = -23 \pm \frac{\cancel{2}i\sqrt{15}}{\cancel{6}3} = -23 \pm \frac{i\sqrt{15}}{3}$$ **Final answer:** $$-23 \pm \frac{i\sqrt{15}}{3}$$