I wouldn't try the bran - that might make the poo situation worse!
Stick to chicken and rice for a few days and see if that clears it up, as the others have suggested. If it does, you'l know it's food related.
We had huge problems when we first had Daisy, and have all bit given up with any kibble now, and she has 99.9% raw diet which has solved the majority of the problems. She has bran in her mince just to keep up with the glands problem, but that's more to do with her distractive nature - she can't sit still after pooing long enough for them to empty

- than her diet!
If after chicken and rice, you have the same problem, then I would suggest a trip to the vet and check it's nothing parasitic such as worms or an infection such as campylobacter.