The sum of 3 consecutive odd numbers and three consecutive even numbers together is 231. Also, the smallest odd number is 11 less than the smallest even number. What is the sum of the largest odd number and the largest even number?

Let's denote the three consecutive odd numbers as x, x+2, x+4 and the three consecutive even numbers as y, y+2, y+4.

According to the problem, we have two equations:

1. x + (x+2) + (x+4) + y + (y+2) + (y+4) = 231
2. x = y - 11

We can simplify the first equation to 3x + 3y + 12 = 231, which further simplifies to x + y = 73.

Substituting the second equation into the simplified first equation, we get y - 11 + y = 73, which simplifies to 2y = 84, so y = 42.

Substituting y = 42 into the second equation, we get x = 42 - 11 = 31.

Therefore, the largest odd number is x+4 = 31+4 = 35 and the largest even number is y+4 = 42+4 = 46.

So, the sum of the largest odd number and the largest even number is 35 + 46 = 81.