Is it possible finding RSA key with only CRT exponents and a prime factor?

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I am learning more RSA and I am facing with this problem.

I have given dp and calculated dq that:

$d \equiv dp (mod (p-1))$
$d \equiv dq (mod (q-1))$

Therefore, now I have a public exponent $e$, a ciphertext $c$ and a prime factor $q$, and two $dp$ and $dq$, all generated from textbook RSA.

As far as I researched, I only can decrypt if I know one more prime factor $p$. However, I haven't found any methods to reverse this from these numbers.

Are there any method to do this? Thank you.