How to remove mini-cart caching in header from Magento 1.9?

Question

Magento

The problem is the following, on the main page it caches the mini basket in the header.
And if you go to the catalog - add a product and go to the main one - the number of products is old.

If you disable fpc , everything is ok.

What I tried is
<?php echo $this->getChildHtml('mini-cartpro',false) ?> in the header.

In reference

<action method="setEsiOptions">
          <params>
            <access>private</access>
            <method>ajax</method>
          </params>
        </action>
        <action method="setCacheLifetime"><s>null</s></action>