As others have mentioned on this subject, in PHP 5.6 you probably don't need the full APC package. Instead, you will almost certainly need a part for caching user data, APCu.
If you are using PECL, you need to specify the correct version of APCu to use, which is apparently 4.0.11:
pecl install apcu-4.0.11
(Worked for me on CentOS 6, EasyApache 3, Apache 2.2, PHP 5.6.39. π)
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