11. (10 points) Among the 6 moments, $6: 30, 6: 31, 6: 32, 6: 33, 6: 34, 6: 35$, the $\qquad$ moment the hour and minute hands are closest, and the $\qquad$ moment the hour and minute hands are farthest.
【Analysis】The minute hand moves $360 \div 60 = 6$ degrees per minute, and the hour hand moves $6 \times 5 \div 60 = 0.5$ degrees per minute. Calculate the degrees moved by the hour and minute hands at 6:30, 6:31, 6:32, 6:33, 6:34, and 6:35, then compare the differences between them to solve the problem.

【Solution】Solution: 6:30 = 390 minutes, 6:31 = 391 minutes, 6:32 = 392 minutes, 6:33 = 393 minutes, 6:34 = 394 minutes, 6:35 = 395 minutes

The minute hand moves
$$
360 \div 60 = 6 \text{ (degrees), }
$$

The hour hand moves
$$
6 \times 5 \div 60 = 0.5 \text{ (degrees), }
$$
At 6:30, the angle between the hour and minute hands:
$$
390 \times 0.5 - 30 \times 6 = 15 \text{ (degrees); }
$$
At 6:31, the angle between the hour and minute hands:
$$
391 \times 0.5 - 31 \times 6 = 9.5 \text{ (degrees); }
$$
At 6:32, the angle between the hour and minute hands:
$$
392 \times 0.5 - 32 \times 6 = 4 \text{ (degrees); }
$$
At 6:33, the angle between the hour and minute hands:
$$
33 \times 6 - 393 \times 0.5 = 1.5 \text{ (degrees); }
$$
At 6:34, the angle between the hour and minute hands:
$$
34 \times 6 - 394 \times 0.5 = 7 \text{ (degrees); }
$$
At 6:35, the angle between the hour and minute hands:
$$
35 \times 6 - 395 \times 0.5 = 12.5 \text{ (degrees); }
$$
$1.5 < 4 < 7 < 9.5 < 12.5 < 15$, so at 6:33, the hour and minute hands are closest, and at 6:30, they are farthest apart. The answer is: 6:33, 6:30.