1. **State the problem:** Add the fractions $\frac{1}{6}$ and $\frac{11}{18}$.\n\n2. **Formula and rules:** To add fractions, they must have a common denominator. The formula is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \neq 0$.\n\n3. **Find the least common denominator (LCD):** The denominators are 6 and 18. The LCD of 6 and 18 is 18.\n\n4. **Convert fractions to have the LCD:**\n$$\frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18}$$\n$$\frac{11}{18} = \frac{11}{18}$$ (already denominator 18)\n\n5. **Add the numerators:**\n$$\frac{3}{18} + \frac{11}{18} = \frac{3 + 11}{18} = \frac{14}{18}$$\n\n6. **Simplify the fraction:**\nThe numerator and denominator share a common factor 2.\n$$\frac{14}{18} = \frac{\cancel{2} \times 7}{\cancel{2} \times 9} = \frac{7}{9}$$\n\n**Final answer:** $$\frac{1}{6} + \frac{11}{18} = \frac{7}{9}$$