Bash conditional or of grep results

I am trying to do a conditional check of the result of two grep commands in a bash script, but I cannot seem to combine them like:

if [[ $( stout_cmd1 | grep -q 'check_txt1' ) || ( $( stdout_cmd2 | grep -q 'check_txt2' ) ]] ; then
    //do something here if output of stdout_cmdX contains text check_txtX
fi

as it always returns false. Conditionally checking the commands on their own work as intended:

if stdout_cmd1 | grep -q 'check_txt1' ; then

or

if stdout_cmd2 | grep -q 'check_txt2' ; then

, but I don't know how to check if either one is true. How does one combine two stdout outputs in a conditional check? I have removed the -q flag from the grep calls with no effect.