The equation presented is:

$-64 = m^3$

To solve for $m$, you need to take the cube root of both sides of the equation. The cube root of a number is the value that, when cubed, gives that number. Here's the step-by-step solution:

$m = \sqrt[3]{-64}$

The cube root of $-64$ is $-4$, because:

$(-4)^3 = -64$

Thus, the solution is:

$m = -4$

Would you like more details or have any questions? Here are five related questions you might want to explore:

1. How do you solve $m^3 = 125$?
2. What is the cube root of a negative number in general?
3. How do you simplify radical expressions involving cubes?
4. What happens when you cube a fraction?
5. Can cube roots ever result in irrational numbers?

Tip: Cube roots of negative numbers are always negative because the cube of a negative number is negative!