As your file residing in your Home directory, I would suggest one of following approaches.
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Give 0777 permission to file itself.
chmod 0777 /home/djameson/test.txt
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Change Ownership to apache user www-data and give owner-write permission.
sudo chown www-data:www-data /home/djameson/test.txt chmod 0744 /home/djameson/test.txt
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Add your user to www-data group or vice-verse add www-data user to your group. And then group write permission.
sudo usermod -a -G www-data djameson chmod 0764 /home/djameson/test.txt
NOTE : I am assuming apache user name & group name is www-data & www-data respectively. You must change accordingly your server apache username/group name.