Yum utility failed to install the required packages installing php-fpm nginx etc

This happens due to two reasons.

1. Plesk is not able to install the package because of bad repository cache

In this case you can fix it using the below steps

yum clean all
rpmdb --rebuilddb
yum update

2. If solution 1 didn’t worked  it seems like the package is not present in the repository

You can fix this by adding atomic repository

wget -q -O - http://www.atomicorp.com/installers/atomic | sh

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