10946 and 17711 are consecutive Fibonacci numbers, so the number that comes next is the sum of these two:
The next Fibonacci number is 10946 + 17711 = 28657
The previous Fibonacci number (I'll call it F for now) fits into the Fibonacci sequence this way:
F + 10946 = 17711
Thus, F = 17711 - 10946 = 6765
Here are some more to try. Find the before and after numbers for each pair:
_________, 46368, 75025, ________
_________, 317811, 514229, ________