How NOT To Require CHMOD 755 Permissions To Create, Write And Delete Files On Linux

On my previous server and on some other hosts, I was able to write to files (for example with PHP) without having to chmod the files first.

Now I cannot, and files are required to be chmoded properly so I can write to them.

I cannot even touch() a file with PHP.

Is there any way to have this permissions removed?

I don't want to chmod the all thing, all I want is to change the configurations so I can fwrite() or file_put_contents() normally.

I's a dedicated un-managed server, so basically any advanced configurations can be done.