\[f(x)=\left \lfloor x-\dfrac{1}{4} \right \rfloor + x \lfloor x \rfloor + | x(x-4) \sin x |+(2x-1)^{\frac{1}{3}}\]

Find the number of points for \(x\in [0,2\pi)\) at which \(f(x)\) is non-differentiable.

**Notations:**

\( \lfloor \cdot \rfloor \) denotes the floor function.

\( | \cdot | \) denotes the absolute value function.

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