mysqldump: command not found

Maybe Your $PATH variable doesn't contain the default paths? echo $PATH should give something like:

[root@server ~]# echo $PATH
/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin:/root/bin

If it's empty, You may set the PATH variable with this command

export PATH="/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin:/root/bin"

On CentOS possible default full paths are:

/usr/bin/mysqldump - from package: mysql55w
/usr/bin/mysqldump - from package: mysql

You may install the required package with command yum install {package}

On Debian possible default full paths are:

/usr/bin/mysqldump - from package: mariadb-client-10.0
/usr/bin/mysqldump - from package: mysql-client-5.5

You may install the required package with command apt-get install {package}

Error in other languages:
mysqldump: bevel nie gevind nie
mysqldump: comandă negăsită
mysqldump: comando não encontrado
mysqldump: commande introuvable
mysqldump: command not found
mysqldump: käsku ei ole
mysqldump: không tìm thấy lệnh
mysqldump: komanda nerasta
mysqldump: Kommando nicht gefunden.
mysqldump: kommandot finns inte
mysqldump: komut yok
mysqldump: nie znaleziono polecenia
mysqldump: níor aimsíodh an t-ordú
mysqldump: no se encontró la orden
mysqldump: no s'ha trobat l'ordre
mysqldump: opdracht niet gevonden
mysqldump: parancs nem található
mysqldump: perintah tidak ditemukan
mysqldump: príkaz nenájdený
mysqldump: příkaz nenalezen
mysqldump: команда не найдена
mysqldump: командата не е открита
mysqldump: 命令找不到
mysqldump: コマンドが見つかりません