Constant current or constant voltage supply? - Setting up LED strips with both series and parallel LEDs on the strips themselves
I suspect the LEDs are used in a mixed arrangement on the strip itself.

They are. The load voltage is 11.2VDC (typ), there are 44 LEDs on a strip, so most likely the LEDs are arranged in 4S11P (11 parallel branches of 4 series LEDs per branch) configuration.

Is it safe to operate strips with mixed connections using a constant current supply?

Yes, it is. Looking at the product picture, there are no resistors, so the strip should be driven with CC. The LEDs should always be driven with CC, though.

We want to use 6 of the mentioned strips in series because normally it is better, ...

The load voltage will be ~78VDC max. So you should check the max output voltage of the LED driver that you are planning to use. It should be higher than 80VDC.

...but if we have parallel connections involved on the strips, CV drive sounds safer because if 1 LED fails the others parallel with the failed one will not overload.

Nope. You need a limiter resistor for CV drive. If you drive a single strip with CV, even if only one LED fails (i.e. goes either short or open), the remaining 10 branches are still in parallel, so the drive current (determined by the limiter series resistor) will be divided into the remaining branches which means kinda overload.
So, go for CC anyways.