Simplify the numerator and the denominator inside the cube root.

The numerator is $0.119 \times 0.256$.
The denominator is $0.068 \times 7$.

$$0.119 \times 0.256 = 0.030464$$ $$0.068 \times 7 = 0.476$$

Convert the decimal to a fraction to find its cube root without a calculator.

$$0.064 = \frac{64}{1000}$$

So the expression becomes:

$$\sqrt[3]{\frac{64}{1000}}$$

$$\sqrt[3]{64} = 4$$ $$\sqrt[3]{1000} = 10$$

$$\frac{4}{10} = \frac{2}{5}$$

The final answer is $\frac{2}{5}$.