Refresh rate not available on clean Linux Mint installation

My laptop has Linux Mint 21.3 installed, with a supported monitor, HDMI cable, and graphics card. It is limited to 3840×2160 30 Hz. I am using Intel(R) XE Graphics.

An existing Windows installation on this computer runs at 3840×2160 at 60.00 Hz.

I would like to run my Linux Mint at 3840×2160 at 60.00 Hz.

I’ve already tried forcing these display settings using cvt and xrandr, to no avail.

Output of xrandr:

Screen 0: minimum 8 x 8, current 3840 x 2160, maximum 32767 x 32767
eDP1 connected (normal left inverted right x axis y axis)
   2560x1600     60.00 +
DP1 disconnected (normal left inverted right x axis y axis)
DP2 disconnected (normal left inverted right x axis y axis)
HDMI1 connected primary 3840x2160+0+0 (normal left inverted right x axis y axis) 940mm x 530mm
   3840x2160     30.00*+  24.00    29.97    23.98  
   4096x2160     30.00    24.00    29.97    23.98  
   1920x1080     60.00    59.94    30.00    24.00    29.97    23.98  
   1680x1050     59.88  
   1280x1024     75.02    60.02  
   1440x900      59.90  
   1280x960      60.00  
   1360x768      60.02  
   1280x800      59.91  
   1152x864      75.00  
   1280x720      60.00    30.00    59.94    29.97    24.00    23.98  
   1024x768      75.03    70.07    60.00  
   800x600       72.19    75.00    60.32  
   720x480       60.00    59.94  
   640x480       75.00    72.81    60.00    59.94  
   720x400       70.08  
VIRTUAL1 disconnected (normal left inverted right x axis y axis)

Thanks for the help.