To find the slant asymptote, we can perform long division or synthetic division to divide $2x^2 + 3x - 7$ by $x - 3$.
The quotient is $2x + 9$ with a remainder of $20$.
So the expression can be written as $y = 2x + 9 + \frac{20}{x - 3}$.
As $x$ approaches $\infty$ or $-\infty$, the last term $\frac{20}{x - 3}$ approaches $0$.
Therefore, the slant asymptote is the line $y = 2x + 9$.
The sum of the coefficients $m$ and $b$ is $2+9=\boxed{11}$.
The answer is: 11
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A slant asymptote of the rational expression $y = \frac{2x^2 + 3x - 7}{x-3}$ is the line approached by the equation as $x$ approaches $\infty$ or $-\infty$. If this line is of the form $y = mx + b$, find $m+b$.

### Answer:
