Querying Serialized Data

I’m attempting to use the meta_value shortcode parameter to query a custom field that contains serialized data. The data are post ids. In order to search as specifically as possible, I need to include quotes, eg, 'meta_value' => '"351"'. This presents a problem with the shortcode because the parameter needs its own double quotes to contain the search string. Is there a way around this? I already tried with html entities.