Those both chown commands you mention should work and are the same. It is
normal with many commands if there is no error you get no output. You can use
the ls -l /sys/class/backlight/intel_backlight/brightness command before and
after the chown command to see the file change owner and group. (from
root:root to jane:jane)
The simplest form without sudo is echo 500 >
/sys/class/backlight/intel_backlight/brightness
however just omitting the sudo word from the longer form should work as well.
I guess it is possible this way does not work for whatever reason. In that
case we can try and come up with another way, if you have the stamina to keep
tinkering. :)