I am running into the same issue and had to dig to correct some errors:
1. Running Apache 2.4.16
2. PHP 5.6.13
3. PHP suEXEC & DSO PHP Handler
4. Apache User/Group = nobody:nobody
5. Moved writable directory above /public_html
a. All paths in configuration.php to /writable_directory are correct
6. Ensure the web server user which has permissions to run under httpd is the same for the writable directory
a. In my case it is nobody
b. Check user for Apache:
c. egrep -iw --color=auto '^user|^group' /etc/httpd/conf/httpd.conf
7. chown -R nobody:nobody /writable_directory
8. In my scenario: suEXEC & DSO, I have had to set directory permissions to 755 not 777
9. Change files within directory to be writable:
a. chmod -R 777 /writable_directory
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Cron jobs are running because I am receiving the email notifications with no permission errors, however I still receive the "Pop Cron Ticket Import" and "System Cron Tasks" errors under the HELP > HEALTH & UPDATES Menu within WHMCS. I am starting to suspect this is a bug.
In any case, this was an upgrade of a pre-existing system. We also have an instance of a new install of WHMCS 6.1 and I will perform some validations to investigate whether this also solves similar issues on that system.
The email message of cron job is "No input file specified." with NO errors.
I will check this evening whether the backup system cron job sends the backup db.
Any relevant information is appreciate, seems like many of us are having the same challenge when upgrading!
@TiOTBiz