In theory since i7-10700 works, i7-10700k would work too.  The -k cpu is creme of crop, heavily binned by intel, the winner of silicon lottery.  But there is not yet material evidence that it does work based on user benchmark validation. 3891 is a new model, newer than XPS8940 (H470) and optiplex 7080 (Q470), both of which support -k cpu.  Optiplex 7090 (Q570) supports -k cpu. A more practical reason why -k cpu not a great idea in 3891: its motherboard has only one 4 pin cpu socket, whereas 8940,7080/7090 all have two 4 pin.  Why do you need two 4 pin.  The -k cpu draws more current than non -k cpu. i7-11700, 16 MB Cache, 8 Core, 16 Threads, 2.5 GHz to 4.9 GHz, 65 W i9-11900, 16 MB Cache, 8 Core, 16 Threads, 2.5 GHz to 5.2 GHz, 65 W  i7-11700K, 16 MB Cache, 8 Core, 16 Threads, 3.6 GHz to 5.0 GHz, 125 W i9-11900K, 16 MB Cache, 8 Core, 16 Threads, 3.5 GHz to 5.3 GHz, 125 W so although the 3891 B560 bios would probably boot the -k cpu, the motherboard is ill equipped to support it.  do not forget Inspiron is for general consumer class not business nor multi purpose XPS.  It is a different class from the more $ optiplex/XPS (although price gap is shrinking).  It has only two dimm slots consistent w lower class as well.  
the motherboard in the inspiron 3891 has a b560 chipset and I'm pretty sure that most, if not all motherboards with a b560 chipset can support i9 and the k series of the intel cpus. so for example, will putting an i7-11700k or an i9-11900/11900k work with this inspiron desktop? or will it not work?
does the inspiron 3891 support intel k series cpu or i9?