Evaluating $\lim_{x\to0}{\frac{\sqrt[3]{\cos{4x}}-\sqrt[3]{\cos{5x}}}{1-\cos{3x}}}$ without L'Hopital's rule

Hint

Use http://mathworld.wolfram.com/ProsthaphaeresisFormulas.html

$$\dfrac{\cos2ax-\cos2bx}{1-\cos2cx}=\dfrac{2\sin(b-a)x\cdot\sin(b+a)x}{2\sin^2cx}$$