To solve the expression \( \frac{1}{4} - \left[ -\frac{6}{5} - \left( -\frac{1}{5} + \frac{3}{4} \right) \right] \), let's follow the order of operations (parentheses, exponents, multiplication/division, and addition/subtraction, also known as PEMDAS/BODMAS).

1. Simplify inside the innermost parentheses first: \( -\frac{1}{5} + \frac{3}{4} \).

To add these fractions, we need a common denominator:
\[
\frac{1}{5} = \frac{4}{20} \quad \text{and} \quad \frac{3}{4} = \frac{15}{20}
\]

Therefore,
\[
-\frac{1}{5} + \frac{3}{4} = -\frac{4}{20} + \frac{15}{20} = \frac{11}{20}
\]

2. Continue simplifying inside the brackets: \( -\frac{6}{5} - \frac{11}{20} \).

To subtract these fractions, we need a common denominator:
\[
\frac{6}{5} = \frac{24}{20}
\]

Therefore,
\[
-\frac{6}{5} - \frac{11}{20} = -\frac{24}{20} - \frac{11}{20} = -\frac{35}{20} = -\frac{7}{4}
\]

3. Now simplify the whole expression: \( \frac{1}{4} - (-\frac{7}{4}) \).

Which simplifies to:
\[
\frac{1}{4} + \frac{7}{4} = \frac{1+7}{4} = \frac{8}{4} = 2
\]

Thus, the resulting value is \( \boxed{2} \).