1. **State the problem:** Solve the equation $$\frac{1}{6}(x + 6) = 11$$ for $x$. 2. **Use the distributive property:** Multiply both sides by 6 to eliminate the fraction. $$6 \times \frac{1}{6}(x + 6) = 6 \times 11$$ 3. **Simplify:** $$\cancel{6} \times \frac{1}{\cancel{6}}(x + 6) = 66$$ which simplifies to $$x + 6 = 66$$ 4. **Isolate $x$:** Subtract 6 from both sides. $$x + 6 - 6 = 66 - 6$$ $$x = 60$$ 5. **Final answer:** $$\boxed{60}$$