How do you save checkbox state in shared preferences after save data button is clicked

I have set up shared preferences to store the values of an ArrayList after a save data button is clicked within my app. This part is working fine.

The trouble I am having is that I have a recyclerview adapter which populates a recyclerview with rows. Each row contains a check box which turns the text in that row green when checked to indicate it has been completed.

My question is how can I add the checkbox state to my shared preferences and save that state so when I re-open the app the checkbox is saved.

Save button in oncreate in main activity

    //Functionality for save button
    final Button saveButton =findViewById(R.id.saveButtonGame);
    saveButton.setOnClickListener(new View.OnClickListener() {
        @Override
        public void onClick(View view) {
            saveData();
        }
    });

Here is my code for my shared preferences in Main Activity (outside oncreate) to save arraylist. How can I implement my checkbox state into this?

//Save data when save button is clicked
private void saveData(){
    SharedPreferences sharedPreferences = getSharedPreferences("shared preferences", MODE_PRIVATE);
    SharedPreferences.Editor editor = sharedPreferences.edit();
    Gson gson = new Gson();
    String json = gson.toJson(gameList);
    editor.putString("game list", json);
    editor.apply();
}

//Load data on app start up
private void loadData(){
    SharedPreferences sharedPreferences = getSharedPreferences("shared preferences", MODE_PRIVATE);
    Gson gson = new Gson();
    String json = sharedPreferences.getString("game list", null);
    Type type = new TypeToken<ArrayList<String>>() {}.getType();
    gameList = gson.fromJson(json, type);

    if(gameList == null){
        gameList = new ArrayList<>();
    }
}