1. **State the problem:** Solve for $m$ in the equation $$1 = 6\sqrt{-19} + 2m - 5$$. 2. **Rewrite the equation:** Add 5 to both sides to isolate terms with $m$: $$1 + 5 = 6\sqrt{-19} + 2m$$ $$6 = 6\sqrt{-19} + 2m$$ 3. **Isolate $2m$:** Subtract $6\sqrt{-19}$ from both sides: $$6 - 6\sqrt{-19} = 2m$$ 4. **Solve for $m$:** Divide both sides by 2: $$m = \frac{6 - 6\sqrt{-19}}{2}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{6} - \cancel{6}\sqrt{-19}}{\cancel{2} \times 1} = 3 - 3\sqrt{-19}$$ 6. **Interpret the square root:** Since $\sqrt{-19} = i\sqrt{19}$ where $i$ is the imaginary unit, the solution is: $$m = 3 - 3i\sqrt{19}$$ **Final answer:** $$m = 3 - 3i\sqrt{19}$$