Doctrine Query from Mysql

I want to create a Doctrine Query: (Doctrine 2.3)

SELECT * FROM `car` WHERE `plate` like '%' AND (`datetime` BETWEEN '2013-03-13 22:20:18' AND '2013-03-13 22:20:20') OR (`datetime` BETWEEN '2013-03-13 15:10:18' AND '2013-03-13 15:10:16')

I tried the following but its not working:

$qry = $this->manager()->createQueryBuilder()
                    ->from($this->entity, 'e')
                    ->select('e');
$qry->where('e.plate like :plate');
$qry->setParameter('plate', $plate);
$qry->andWhere(
        qry->expr()->between(
             'e.datetime',
            ':dateFrom',
            ':dateTo'
         )
        )
    ->setParameter('dateFrom', $fromdate)
    ->setParameter('dateTo', $todate);
    $qry->orWhere(
            $qry->expr()->between(
                'e.datetime',
                ':dateFrom',
                ':dateTo'
             )
            )
    ->setParameter('dateFrom1', $fromdate1)
    ->setParameter('dateTo1', $todate1);

OutPut of above query:

SELECT e FROM user e WHERE (e.plate like :plate AND (e.datetime BETWEEN :dateFrom AND :dateTo)) OR (e.datetime BETWEEN :dateFrom AND :dateTo)

I want to check two dates in same column how can I check? Is the syntax correct? Currently It is like this:

(Plate AND (Date)) OR Date)

Case 1

But it should come like the following for good output.

(Plate) AND ((Date) OR (Date))

Case 2

In other case it should come like this:

((Plate) or (Plate)) AND ((Date) OR (Date))

Can some one help me I am not an expert in Doctrine I am a learner!

After some search and advice from many individual I finally found some logic and understood the expression in Doctrine. Below I have given all the expression with an example. Code to be tested.

$ex1    =   $qry->expr()->like('e.user', "'".$user."'");
$ex2    =   $qry->expr()->orX(
                $qry->expr()->between('e.datetime', "'".$datetimefrom."'", "'".$datetimeto."'")
            );
$ex3    =   $qry->expr()->in('e.country', $country);
$final_expression = $qry->expr()->andX($ex1,$ex2,$ex3);

You can also refer the below issue and solution which helped me to solve the above Question by me.

REF Multiple Query in Doctrine with NAND,NOR,NOT,AND Operators