Let's start by solving the equation:
\[ 11x = 3(7x - 1) - 10x \]
First, distribute the 3 on the right-hand side:
\[ 11x = 21x - 3 - 10x \]
Now, combine like terms on the right side:
\[ 11x = (21x - 10x) - 3 \]
This simplifies to:
\[ 11x = 11x - 3 \]
Next, subtract \(11x\) from both sides:
\[ 11x - 11x = 11x - 3 - 11x \] \[ 0 = -3 \]
This statement, \(0 = -3\), is a contradiction and is not true. Therefore, this indicates that there are no solutions to the equation.
So the answer is: The equation has no solution.