Step 1: Express everything in terms of \(11!\)
\[ 9! = \frac{11!}{11 \cdot 10}, \quad 10! = \frac{11!}{11} \] So: \[ \frac{1}{9!} = \frac{11 \cdot 10}{11!} = \frac{110}{11!}, \quad \frac{1}{10!} = \frac{11}{11!} \]

Step 2: Add the fractions
\[ \frac{1}{9!} + \frac{1}{10!} = \frac{110}{11!} + \frac{11}{11!} = \frac{121}{11!} \]

Step 3: Compare with \(\frac{x}{11!}\)
\[ x = 121 \]