Yum dependency conflict in ImageMagick update

I am running a Lamp server on CentOS release 6.6 (Final) with php5.5:

$ php -v
PHP 5.5.17 (cli) (built: Sep 20 2014 17:12:00)
Copyright (c) 1997-2014 The PHP Group
Zend Engine v2.5.0, Copyright (c) 1998-2014 Zend Technologies
with Zend OPcache v7.0.4-dev, Copyright (c) 1999-2014, by Zend Technologies
with Xdebug v2.2.5, Copyright (c) 2002-2014, by Derick Rethans

When I run yum update I get this dependency error:

Loaded plugins: fastestmirror
Setting up Update Process
Loading mirror speeds from cached hostfile
 * webtatic: uk.repo.webtatic.com
Resolving Dependencies
--> Running transaction check
---> Package libwebp.x86_64 0:0.3.1-2.el6.remi will be updated
--> Processing Dependency: libwebp.so.4()(64bit) for package: ImageMagick-last-libs-6.8.9.7-4.el6.remi.x86_64
---> Package libwebp.x86_64 0:0.4.3-3.el6 will be an update
--> Finished Dependency Resolution
Error: Package: ImageMagick-last-libs-6.8.9.7-4.el6.remi.x86_64 (@remi)
           Requires: libwebp.so.4()(64bit)
           Removing: libwebp-0.3.1-2.el6.remi.x86_64 (@remi)
               libwebp.so.4()(64bit)
           Updated By: libwebp-0.4.3-3.el6.x86_64 (epel)
               Not found
 You could try using --skip-broken to work around the problem
 You could try running: rpm -Va --nofiles --nodigest

My vague understanding of this is that the ImageMagick update requires libwebp.so.4, but I have libwebp-0.3.1-2.el6.remi.x86_64 from the @remi rpm but this has since been updated to libwebp-0.4.3-3.el6.x86_64 from the epel rpm.

Is that correct? If not what does the above output mean?

And more importantly how might I fix this?