To solve the first equation:

9(3x-7) + 3(8x-11) = 3(9x+8)
27x - 63 + 24x - 33 = 27x + 24
51x - 96 = 27x + 24
51x - 27x = 96 + 24
24x = 120
x = 120 / 24
x = 5

Therefore, the solution to the first equation is x = 5.

To solve the second equation:

6(7x-11) - 13(x-6) = 14(2x+1)
42x - 66 - 13x + 78 = 28x + 14
29x + 12 = 28x + 14
29x - 28x = 14 - 12
x = 2

Therefore, the solution to the second equation is x = 2.