To solve the equation \( 321 - \left(\frac{x}{11} + 29\right) \cdot 6 = 105 \), we can follow these steps:
First, isolate the term containing \( x \): \[ 321 - 105 = \left(\frac{x}{11} + 29\right) \cdot 6 \] \[ 216 = \left(\frac{x}{11} + 29\right) \cdot 6 \]
Next, divide both sides by 6: \[ \frac{216}{6} = \frac{x}{11} + 29 \] \[ 36 = \frac{x}{11} + 29 \]
Now, subtract 29 from both sides: \[ 36 - 29 = \frac{x}{11} \] \[ 7 = \frac{x}{11} \]
Finally, multiply both sides by 11 to solve for \( x \): \[ x = 7 \cdot 11 \] \[ x = 77 \]
Thus, the solution is \( x = 77 \).