Let's break down the expression step by step to simplify it:

\[ \frac{11}{8} \left[ \left( -\frac{5}{11} \div \frac{13}{8} - \frac{5}{11} \div \frac{13}{5} \right) + -\frac{6}{33} \right] + \frac{3}{4} \]

First, we need to handle the divisions inside the brackets. Recall that dividing by a fraction is the same as multiplying by its reciprocal.

1. Calculate \( -\frac{5}{11} \div \frac{13}{8} \):
\[ -\frac{5}{11} \div \frac{13}{8} = -\frac{5}{11} \times \frac{8}{13} = -\frac{5 \times 8}{11 \times 13} = -\frac{40}{143} \]

2. Calculate \( -\frac{5}{11} \div \frac{13}{5} \):
\[ -\frac{5}{11} \div \frac{13}{5} = -\frac{5}{11} \times \frac{5}{13} = -\frac{5 \times 5}{11 \times 13} = -\frac{25}{143} \]

Now, substitute these results back into the expression inside the brackets:

\[ \left( -\frac{40}{143} - \frac{25}{143} \right) + -\frac{6}{33} \]

Combine the fractions with a common denominator:

\[ -\frac{40}{143} - \frac{25}{143} = -\frac{40 + 25}{143} = -\frac{65}{143} \]

Next, simplify \(-\frac{6}{33}\):

\[ -\frac{6}{33} = -\frac{2}{11} \]

Now, we need a common denominator to combine \(-\frac{65}{143}\) and \(-\frac{2}{11}\). The least common multiple of 143 and 11 is 143:

\[ -\frac{2}{11} = -\frac{2 \times 13}{11 \times 13} = -\frac{26}{143} \]

Combine the fractions:

\[ -\frac{65}{143} + -\frac{26}{143} = -\frac{65 + 26}{143} = -\frac{91}{143} \]

Now, multiply by \(\frac{11}{8}\):

\[ \frac{11}{8} \times -\frac{91}{143} = -\frac{11 \times 91}{8 \times 143} = -\frac{1001}{1144} \]

Finally, add \(\frac{3}{4}\):

Convert \(\frac{3}{4}\) to a fraction with a common denominator of 1144:

\[ \frac{3}{4} = \frac{3 \times 286}{4 \times 286} = \frac{858}{1144} \]

Combine the fractions:

\[ -\frac{1001}{1144} + \frac{858}{1144} = \frac{-1001 + 858}{1144} = \frac{-143}{1144} \]

Simplify the fraction:

\[ \frac{-143}{1144} = -\frac{1}{8} \]

So, the simplified result is:

\[ -\frac{1}{8} \]