What is the value of $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{3}{7}+\frac{8}{12}\div\frac{6}{24}+\frac{5}{7}\right]}{\frac{3}{12}\times\ \frac{6}{5}}$$?

= $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{3}{7}+\frac{8}{12}\div\frac{6}{24}+\frac{5}{7}\right]}{\frac{3}{12}\times\ \frac{6}{5}}$$

= $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{3}{7}+\frac{8}{12}\times\frac{24}{6}+\frac{5}{7}\right]}{\frac{1}{2}\times\ \frac{3}{5}}$$

= $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{3}{7}+\frac{8}{3}+\frac{5}{7}\right]}{\frac{3}{10}}$$

= $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{8}{7}+\frac{8}{3}\right]}{\frac{3}{10}}$$

= $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{24}{21}+\frac{56}{21}\right]}{\frac{3}{10}}$$

= $$\frac{\frac{5}{6}-\frac{5}{11}of\left[\frac{80}{21}\right]}{\frac{3}{10}}$$

= $$\frac{\frac{5}{6}-\frac{5}{11}\times\ \frac{80}{21}}{\frac{3}{10}}$$

= $$\frac{\frac{5}{6}-\frac{400}{231}}{\frac{3}{10}}$$

= $$\frac{\frac{385}{462}-\frac{800}{462}}{\frac{3}{10}}$$

= $$-\frac{415}{462}\times\ \frac{10}{3}$$

= $$-\frac{415}{231}\times\ \frac{5}{3}$$

= $$-\frac{2075}{693}$$