Percentiles and Box Plots · Superchallenge problem

A whole number $x$ is added to the data $12, 15, 17, 20, 22, 25, 30$, making eight values ($Q_1$ and $Q_3$ are the medians of the lower four and upper four). The interquartile range depends on $x$. What is the sum of all whole numbers $x$ for which the IQR is as small as possible?