The pace (or speed) at which you run is governed by both cadence and stride length. Your cadence need not increase dramatically when you're running significantly faster. Here is some data taken from two of my runs this week:
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As you can see, my stride length is really what changed between them, while my cadence remained roughly the same.
The stride length and cadence data above was taken from a Garmin HRM-RUN4 chest strap paired with a FR630. However, I've never had any issues with how the FR235 tracked my cadence with its built-in accelerometer, in the year that I've used it.