$6\frac{3}{11} + x = 10\frac{6}{7}$
$x = 10\frac{66}{77} - 6\frac{21}{77}$
$x = 4\frac{45}{77}$

$9\frac{5}{36} - x = 2\frac{4}{9}$
$x = 9\frac{5}{36} - 2\frac{16}{36}$
$x = 8\frac{41}{36} - 2\frac{16}{36}$
$x = 6\frac{25}{36}$

$x - 5\frac{17}{60} = 7\frac{9}{20}$
$x = 7\frac{27}{60} + 5\frac{17}{60}$
$x = 12\frac{44}{60} = 12\frac{11}{15}$