Решение:

$$(z + \frac{5}{12}) - \frac{9}{20} = \frac{11}{15}$$ $$z + \frac{5}{12} = \frac{11}{15} + \frac{9}{20}$$ $$z + \frac{5}{12} = \frac{44}{60} + \frac{27}{60} = \frac{71}{60}$$ $$z = \frac{71}{60} - \frac{5}{12} = \frac{71}{60} - \frac{25}{60} = \frac{46}{60} = \frac{23}{30}$$

Ответ: \(z = \frac{23}{30}\)