Unable to POST to a specific site using cURL

I'm trying to POST some form data to a site using cURL. It's not a secure site, and doesn't require logging in. It's just a form used to get back some information.

When I post the form manually inside the given web site, I can inspect the headers that are sent. I've tried in vain to reproduce them using cURL. This is normally not a problem for me, but I'm reaching out to others who might know how to do this successfully.

The URL is: http://ift.tt/1HtMOKc, and the form action is to the same page (it's in Turkish).

Here are valid form inputs:

Şehir: ADANA
İlçe: SARIÇAM
Okul: Hacı Özcan Sinağ Ortaokulu
Sınav Türü: TEOGS | ADANA İL MİLLİ EĞİTİM OKDS
Sınıf: 8
Öğrenci No: 1941
Öğrenci Ad: BERKANT İPEK

Here is what the form looks like filled out:

Here are the form headers taken from Chrome on a successful POST request:

POST /index.php HTTP/1.1
Host: objektifsonuc.com
Connection: keep-alive
Content-Length: 138
Cache-Control: max-age=0
Origin: http://ift.tt/1EfRaFe
User-Agent: Mozilla/5.0 (Windows NT 6.2; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/41.0.2272.118 Safari/537.36
Content-Type: application/x-www-form-urlencoded
DNT: 1
Referer: http://ift.tt/1HtMOKc
Accept-Encoding: gzip, deflate
Accept-Language: en-US,en;q=0.8
Cookie: PHPSESSID=veb6h5ht0nqk1pu4d46sbvpch3

And here is the POST body:

il=1&ilce=1%3B18&okul=1%3B18%3B743729%3BTEOGS%2CSBS&sinav=100%3BTEOGS&sinif=8&ogrno=1941&ograd=BERKANT+%DDPEK&ogr=%D6%F0renci+Veli+Giri%FE

This is how I have been trying to send a POST request in PHP:

$headers = array(
    "content-length: 138",
    "cookie: PHPSESSID=veb6h5ht0nqk1pu4d46sbvpch3;",
    "accept-language: en-US,en;q=0.8",
    "accept-encoding: gzip, deflate",
    "referer: http://ift.tt/1EfRaFe",
    "dnt: 1",
    "content-type: application/x-www-form-urlencoded",
    "user-agent: Mozilla/5.0 (Windows NT 6.2; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/41.0.2272.118 Safari/537.36",
    "origin: http://ift.tt/1EfRaFe",
    "accept: text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,*/*;q=0.8",
    "cache-control: max-age=0",
    "connection: keep-alive"
    "host: objektifsonuc.com"
);

$query="il=1&ilce=1%3B18&okul=1%3B18%3B743729%3BTEOGS%2CSBS&sinav=100%3BTEOGS&sinif=8&ogrno=1941&ograd=BERKANT+%DDPEK&ogr=%D6%F0renci+Veli+Giri%FE";

$url = "http://ift.tt/1HtMOKc";

$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_POSTFIELDS, $query);
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
curl_setopt($ch, CURLOPT_FOLLOWLOCATION, true);
echo curl_exec($ch);

Current result: The form page renders

Desired result: A different page containing some tables renders

I'm stumped. What is causing the POST to fail? Can anyone make this POST succeed?