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NE5532: Oscillating in circuit

Part Number: NE5532

Following the directions in the datasheet for the Linear LTC1968, I implemented a Sallen-Key filter with buffer as per the attached schematic.

When I model the circuit in LTSpice, it works fine and is stable. On the PCB, however, it nicely oscillates with a 400 kHz, 1V p-p sine wave. I've tried and I can't make it do that in LTSpice. It's obviously a layout problem, but any suggestions on where to look and how to fix would be greatly appreciated. On the board, all components are SMT. What I did notice is that R11, R12, and R13 are set close together, and putting a finger close to them affects the oscillation, usually increasing it, so it's probably capacitive coupling somewhere.