1. **State the problem:** Two numbers have a sum of 11. One of the numbers is $m$. Find the other number. 2. **Write the equation:** Let the other number be $x$. The sum of the two numbers is given by: $$m + x = 11$$ 3. **Isolate the unknown:** To find $x$, subtract $m$ from both sides: $$x = 11 - m$$ 4. **Explain:** Since the sum of the two numbers is 11, and one number is $m$, the other number must be whatever remains when you subtract $m$ from 11. 5. **Final answer:** The other number is: $$\boxed{11 - m}$$