In order to retrieve all the root folders that a specific user can see you will have to invoke the findByProperties2 web service, providing the following JSON:

{
    "client": {
        "clientId": "clientIdHere"
    },
    "properties": {
        "categoryTypes": ["PUBLIC"],
        "excludeLevelHigherThan": 1
    },
    "locale": "EN",
    "offset": 0,
    "orderBy": "categoryName_A",
    "numberOfResult": 50,
    "categoryFieldOption": {
        "returnNumberOfContents": false,
        "returnNumberOfUnreadContents": false,
        "returnNumberOfUnreadContentsInSubCategories": false,
        "returnNumberOfSubCategories": true
    }
}